Homework 1
Linear Regression
The data for this problem illustrate the relationship between the average monthly outdoor temperature (in degrees Fahrenheit) and the average monthly gas consumption (in therms) for a household. Use the attached SAS output to answer the following questions.
The
SAS System
Plot of
avgas*avtemp.
Legend: A = 1 obs, B = 2 obs,
etc.
12 ˆ
‚
A
A
‚
‚
‚
‚ A
‚
10 ˆ
‚ A
‚
A
‚
‚
A
‚
‚
8 ˆ A
‚
‚ A A
avgas
‚
‚
‚
‚
6 ˆ
‚ A
‚
‚ A
‚
‚
‚
4 ˆ
‚
‚
A
‚
A
‚
‚
‚
2 ˆ
A
‚
‚
A
‚
‚
A
‚
‚
0 ˆ
Šˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒ
25
30 35 40
45 50 55
60 65 70
75
avtemp
The SAS
System
Obs time
avtemp
avgas
1 0 29
8.9
2 1 30
11.6
3 2 31
10.7
4 3 37
11.6
5 4 48
7.5
6 5 57
3.5
7 6 68
1.5
8 8 71 0.8
9 10 53
1.9
10 11 40
5.0
11 12 39
7.3
12 13
29 9.3
13 14
36 9.7
14 15
37 7.9
15 16
46 5.8
16 17
56 3.2
The
CORR Procedure
2 Variables: avgas
avtemp
Pearson
Correlation Coefficients, N = 16
Prob > |r| under H0:
avgas avtemp
avgas 1.00000
-0.90300
avtemp -0.90300 1.00000
The
REG Procedure
Model:
MODEL1
Dependent
Variable: avgas
Analysis
of Variance
Sum of Mean
Source DF Squares Square F Value
Pr > F
Model 1 161.51498 161.51498 61.85
<.0001
Error 14 36.56252 2.61161
Corrected Total 15 198.07750
Root MSE 1.61605 R-Square
0.8154
Dependent Mean 6.63750 Adj R-Sq 0.8022
Coeff
Var
24.34723
Parameter Estimates
Parameter Standard
Variable DF
Estimate Error t Value
Pr > |t|
Intercept 1
17.37277 1.42362 12.20
<.0001
avtemp
1 -0.24295 0.03089 -7.86
<.0001
The
SAS System
Plot
of res*pred. Legend: A = 1 obs,
B = 2 obs, etc.
4 ˆ
‚
‚
‚
‚
‚
A
3 ˆ
‚
‚
‚
‚
‚
2 ˆ
‚ A
‚
‚
A
‚
R
‚
e 1 ˆ
A
s ‚
A
i ‚
A A
d ‚
u ‚
a ‚
l 0 ˆ A
‚
‚ A
‚ A A
‚
A
‚
-1 ˆ
A
‚
‚
‚
A
‚
‚
-2 ˆ
‚
‚
‚
‚ A A
‚
-3 ˆ
Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ
0 2 4 6 8 10 12
Predicted Value of avgas
Plot of res*time. Legend: A = 1 obs,
B = 2 obs, etc.
4 ˆ
‚
‚
‚
‚
‚ A
3 ˆ
‚
‚
‚
‚
‚
2 ˆ
‚ A
‚
‚
A
‚
R ‚
e 1 ˆ
A
s ‚
A
i ‚ A A
d ‚
u ‚
a ‚
l 0 ˆ A
‚
‚
A
‚
A A
‚
A
‚
-1 ˆ
A
‚
‚
‚ A
‚
‚
-2 ˆ
‚
‚
‚
‚
A A
‚
-3 ˆ
Šƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒƒƒˆƒƒ
0
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17
time